NAG Library Function Document

nag_cumul_normal_complem (s15acc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_cumul_normal_complem (s15acc) returns the value of the complement of the cumulative Normal distribution function, Qx.

2
Specification

#include <nag.h>
#include <nags.h>
double  nag_cumul_normal_complem (double x)

3
Description

nag_cumul_normal_complem (s15acc) evaluates an approximate value for the complement of the cumulative Normal distribution function
Qx=12πxe-u2/2du.  
The function is based on the fact that
Qx=12erfcx2  
and it calls nag_erfc (s15adc) to obtain the necessary value of erfc, the complementary error function.

4
References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5
Arguments

1:     x doubleInput
On entry: the argument x of the function.

6
Error Indicators and Warnings

None.

7
Accuracy

Because of its close relationship with erfc the accuracy of this function is very similar to that in nag_erfc (s15adc). If ε and δ are the relative errors in result and argument, respectively, then in principle they are related by
ε x e -x2/2 2πQx δ .  
For x negative or small positive this factor is always less than one and accuracy is mainly limited by machine precision. For large positive x we find εx2δ and hence to a certain extent relative accuracy is unavoidably lost. However the absolute error in the result, E, is given by
E x e -x2/2 2π δ  
and since this factor is always less than one absolute accuracy can be guaranteed for all x.

8
Parallelism and Performance

nag_cumul_normal_complem (s15acc) is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

10.1
Program Text

Program Text (s15acce.c)

10.2
Program Data

Program Data (s15acce.d)

10.3
Program Results

Program Results (s15acce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017